Entropy, stability and harmonic map flow
نویسندگان
چکیده
منابع مشابه
Rigidity in the Harmonic Map Heat Flow
We establish various uniformity properties of the harmonic map heat ow, including uniform convergence in L 2 exponentially as t ! 1, and uniqueness of the positions of bubbles at innnite time. Our hypotheses are that the ow is between 2-spheres, and that the limit map and any bubbles share the same orientation.
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In this paper, we construct a new type of singularity which may occur in weak solutions of the harmonic map flow for two-dimensional domains. This " reverse bubbling " singu-larity may occur spontaneously, and enables us to construct solutions to the harmonic map heat equation which differ from the standard Struwe solution, despite agreeing for an arbitrarily long initial time interval.
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We present an analysis of bounded-energy low-tension maps between 2-spheres. By deriving sharp estimates for the ratio of length scales on which bubbles of opposite orientation develop, we show that we can establish a ‘quantization estimate’ which constrains the energy of the map to lie near to a discrete energy spectrum. One application is to the asymptotics of the harmonic map flow; we find u...
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Abstract. Let B1 be the unit open disk in R2 and M be a closed Riemannian manifold. In this note, we first prove the uniqueness for weak solutions of the harmonic map heat flow in H1([0, T ]×B1,M) whose energy is non-increasing in time, given initial data u0 ∈ H(B1,M) and boundary data γ = u0|∂B1 . Previously, this uniqueness result was obtained by Rivière (when M is the round sphere and the en...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2017
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6949